Prime p₀= 1241058085966037639 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 58 2 40 2 4 2 40 2 58 2 (?)
a_n: 0 2 60 62 102 104 108 110 150 152 210 212
All 12 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 212
Found by: Cruncher Pete
db: batch=77, k=12, 2 58 2 40 2 4

STPT(10)	1241056726138268951	0 2 6 8 18 20 30 32 36 38	-1359827768688
SPT(16)	1241056781823460333	0 4 28 36 78 88 114 120 124 130 156 166 208 216 240 244	-1304142577306
SPT(13)	1241056947961331167	0 30 60 84 90 144 150 156 210 216 240 270 300	-1138004706472
SPT(16)	1241057152641859711	0 28 36 48 60 88 100 162 166 228 240 268 280 292 300 328	-933324177928
STPT(10)	1241057348833600931	0 2 6 8 48 50 90 92 96 98	-737132436708
SPT(16)	1241057484456983939	0 92 182 252 270 278 284 344 348 408 414 422 440 510 600 692	-601509053700
SPT(16)	1241058179910434533	0 36 40 64 70 76 180 196 294 310 414 420 426 450 454 490	93944396894
SPT(16)	1241058262305771017	0 14 26 42 54 80 150 162 194 206 276 302 314 330 342 356	176339733378
SPT(16)	1241058385555732067	0 2 24 30 44 102 120 122 252 254 272 330 344 350 372 374	299589694428
TPT(14)	1241058391542707147	0 2 54 56 60 62 90 92 132 134 174 176 180 182	305576669508
STPT(10)	1241058467437622159	0 2 18 20 30 32 42 44 60 62	381471584520